| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19301 |
\begin{align*}
y-x y^{2}+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.273 |
|
| 19302 |
\begin{align*}
{x^{\prime }}^{2}-t x+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.273 |
|
| 19303 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.273 |
|
| 19304 |
\begin{align*}
\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.276 |
|
| 19305 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.281 |
|
| 19306 |
\begin{align*}
m v^{\prime }&=m g -k v^{2} \\
v \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.287 |
|
| 19307 |
\begin{align*}
y^{\prime }&=\frac {32 y x^{5}+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.288 |
|
| 19308 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.289 |
|
| 19309 |
\begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.289 |
|
| 19310 |
\begin{align*}
x&=t x^{\prime }+\frac {1}{x^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.290 |
|
| 19311 |
\begin{align*}
y-1+x \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.291 |
|
| 19312 |
\begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.292 |
|
| 19313 |
\begin{align*}
y^{\prime }&=-\frac {i \left (i x +x^{4}+2 y^{2} x^{2}+y^{4}\right )}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.293 |
|
| 19314 |
\begin{align*}
x +y y^{\prime }+\frac {-y+y^{\prime } x}{x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.293 |
|
| 19315 |
\begin{align*}
x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.293 |
|
| 19316 |
\begin{align*}
2 y y^{\prime } x&=y^{2}+a x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.294 |
|
| 19317 |
\begin{align*}
x^{3} y^{\prime }&=2 y^{2}+2 x^{2} y-2 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.296 |
|
| 19318 |
\begin{align*}
v^{\prime }&=-\frac {v}{R C} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.298 |
|
| 19319 |
\begin{align*}
x^{6} {y^{\prime }}^{3}-3 y^{\prime } x -3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.299 |
|
| 19320 |
\begin{align*}
y^{\prime }&=y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
7.300 |
|
| 19321 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.302 |
|
| 19322 |
\begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.302 |
|
| 19323 |
\begin{align*}
y^{\prime \prime } x +y \ln \left (1-x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.302 |
|
| 19324 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.303 |
|
| 19325 |
\begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.306 |
|
| 19326 |
\begin{align*}
x^{2} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.308 |
|
| 19327 |
\begin{align*}
x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
7.308 |
|
| 19328 |
\begin{align*}
6 y-4 \left (a +x \right ) y^{\prime }+\left (a +x \right )^{2} y^{\prime \prime }&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.308 |
|
| 19329 |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.308 |
|
| 19330 |
\begin{align*}
t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.309 |
|
| 19331 |
\begin{align*}
3 y x +2 y^{2}+y+\left (x^{2}+2 y x +x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.312 |
|
| 19332 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.312 |
|
| 19333 |
\begin{align*}
2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.315 |
|
| 19334 |
\begin{align*}
y y^{\prime }-{\mathrm e}^{\frac {x}{y}} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.316 |
|
| 19335 |
\begin{align*}
y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.320 |
|
| 19336 |
\begin{align*}
y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.320 |
|
| 19337 |
\begin{align*}
y&=x +3 \ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.321 |
|
| 19338 |
\begin{align*}
x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.323 |
|
| 19339 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.323 |
|
| 19340 |
\begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.323 |
|
| 19341 |
\begin{align*}
2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.325 |
|
| 19342 |
\begin{align*}
{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.325 |
|
| 19343 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 y^{2} x^{2}+7 x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.326 |
|
| 19344 |
\begin{align*}
y^{\prime }-6 y&={\mathrm e}^{6 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.328 |
|
| 19345 |
\begin{align*}
y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.332 |
|
| 19346 |
\begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.333 |
|
| 19347 |
\begin{align*}
4 y+y^{\prime \prime }&=8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.335 |
|
| 19348 |
\begin{align*}
y^{\prime }&=\frac {y}{1+t}+4 t^{2}+4 t \\
y \left (1\right ) &= 10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.339 |
|
| 19349 |
\begin{align*}
{\mathrm e}^{y x} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{y x}+3 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.340 |
|
| 19350 |
\begin{align*}
L y^{\prime }+R y&=E \sin \left (\omega x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.340 |
|
| 19351 |
\begin{align*}
y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.342 |
|
| 19352 |
\begin{align*}
\theta ^{\prime \prime }-p^{2} \theta &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.344 |
|
| 19353 |
\begin{align*}
2 y^{\prime }&=3 \left (-2+y\right )^{{1}/{3}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.345 |
|
| 19354 |
\begin{align*}
a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.345 |
|
| 19355 |
\begin{align*}
y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.346 |
|
| 19356 |
\begin{align*}
y^{\prime } x -y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.347 |
|
| 19357 |
\begin{align*}
y^{\prime } x -y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.348 |
|
| 19358 |
\begin{align*}
y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.350 |
|
| 19359 |
\begin{align*}
y^{\prime }&=k y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.355 |
|
| 19360 |
\begin{align*}
x^{2} y^{\prime \prime }+y&=16 \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.356 |
|
| 19361 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+8 y&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.356 |
|
| 19362 |
\begin{align*}
{y^{\prime }}^{2}&=a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.361 |
|
| 19363 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=-2 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.363 |
|
| 19364 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.364 |
|
| 19365 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.365 |
|
| 19366 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.365 |
|
| 19367 |
\begin{align*}
y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-2 \left (-1+x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.371 |
|
| 19368 |
\begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.372 |
|
| 19369 |
\begin{align*}
y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.373 |
|
| 19370 |
\begin{align*}
y^{\prime \prime \prime }-y&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.377 |
|
| 19371 |
\begin{align*}
\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.379 |
|
| 19372 |
\begin{align*}
y^{\prime \prime }-k^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.382 |
|
| 19373 |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.384 |
|
| 19374 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
7.384 |
|
| 19375 |
\begin{align*}
y^{\prime }&=\frac {x y}{x^{2}+1} \\
y \left (\sqrt {15}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.390 |
|
| 19376 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.395 |
|
| 19377 |
\begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.397 |
|
| 19378 |
\begin{align*}
y^{\prime }&=2 y \left (1-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.398 |
|
| 19379 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.401 |
|
| 19380 |
\begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.402 |
|
| 19381 |
\begin{align*}
y^{\prime }+\tan \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.402 |
|
| 19382 |
\begin{align*}
y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.403 |
|
| 19383 |
\begin{align*}
y^{\prime }+\frac {4 y}{-1+x}&=\frac {1}{\left (-1+x \right )^{5}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.404 |
|
| 19384 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.404 |
|
| 19385 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.408 |
|
| 19386 |
\begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.408 |
|
| 19387 |
\begin{align*}
y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\
y \left (2\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.408 |
|
| 19388 |
\begin{align*}
y^{\prime }+20 y&=24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.408 |
|
| 19389 |
\begin{align*}
\left (1-x^{2} y\right ) y^{\prime }+1-x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.409 |
|
| 19390 |
\begin{align*}
y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.411 |
|
| 19391 |
\begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.411 |
|
| 19392 |
\begin{align*}
\operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
7.414 |
|
| 19393 |
\begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.414 |
|
| 19394 |
\begin{align*}
-y^{\prime } x +y&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.417 |
|
| 19395 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.419 |
|
| 19396 |
\begin{align*}
2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.419 |
|
| 19397 |
\begin{align*}
x^{4} \left (x^{2}+1\right ) \left (-1+x \right )^{2} y^{\prime \prime }+4 x^{3} \left (-1+x \right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
7.422 |
|
| 19398 |
\begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.424 |
|
| 19399 |
\begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.424 |
|
| 19400 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.427 |
|